$\dfrac{ -10d + e }{ 2 } = \dfrac{ -d - f }{ 3 }$ Solve for $d$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -10d + e }{ {2} } = \dfrac{ -d - f }{ 3 }$ ${2} \cdot \dfrac{ -10d + e }{ {2} } = {2} \cdot \dfrac{ -d - f }{ 3 }$ $-10d + e = {2} \cdot \dfrac { -d - f }{ 3 }$ Multiply both sides by the right denominator. $-10d + e = 2 \cdot \dfrac{ -d - f }{ {3} }$ ${3} \cdot \left( -10d + e \right) = {3} \cdot 2 \cdot \dfrac{ -d - f }{ {3} }$ ${3} \cdot \left( -10d + e \right) = 2 \cdot \left( -d - f \right)$ Distribute both sides ${3} \cdot \left( -10d + e \right) = {2} \cdot \left( -d - f \right)$ $-{30}d + {3}e = -{2}d - {2}f$ Combine $d$ terms on the left. $-{30d} + 3e = -{2d} - 2f$ $-{28d} + 3e = -2f$ Move the $e$ term to the right. $-28d + {3e} = -2f$ $-28d = -2f - {3e}$ Isolate $d$ by dividing both sides by its coefficient. $-{28}d = -2f - 3e$ $d = \dfrac{ -2f - 3e }{ -{28} }$ Swap signs so the denominator isn't negative. $d = \dfrac{ {2}f + {3}e }{ {28} }$